Generation and interference collapse of distortion-less fs pulses in free space by Fresnel sources

A method of formation of the tightly confined, distortion-free, femtosecond pulses in two dimensions (2D) with the step-like decreasing of intensity after a finite length of propagation in free space is described. The pulses are formed by the Fresnel source of modes corresponding to a 2D hollow waveguide with perfectly reflecting walls (material waveguide). The source reproduces in free space a propagation-invariant pulse confined by the waveguide. Unlike the case of material waveguides, when the pulse goes out from the virtual waveguide formed by the Fresnel source its shape does not change, but the intensity immediately drops down to the near-zero level. It is also shown that there is a limit of the duration of pulse beyond which the step-like decay is not observed.